A population proportion is 0.4. A sample of size 200 will be taken and the sample proportion p will be used to estimate the population proportion. Use z- table Round your answers to four decimal places. Do not round intermediate calculations. a. What is the probability that the sample proportion will be within ±0.03 of the population proportion? b. What is the probability that the sample proportion will be within ±0.08 of the population proportion?

Answer:

A) 0.61351

Step-by-step explanation:

Sample proportion = 0.4

Sample population = 200

A.) proprobaility that sample proportion 'p' is within ±0.03 of population proportion

Statistically:

P(0.4-0.03<p<0.4+0.03)

P[((0.4-0.03)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.03)-0.4)/√((0.4)(.6))/200

P[-0.03/0.0346410 < z < 0.03/0.0346410

P(−0.866025 < z < 0.866025)

P(z < - 0.8660) - P(z < 0.8660)

0.80675 - 0.19325

= 0.61351

B) proprobaility that sample proportion 'p' is within ±0.08 of population proportion

Statistically:

P(0.4-0.08<p<0.4+0.08)

P[((0.4-0.08)-0.4)/√((0.4)(.6))/200 < z < ((0.4+0.08)-0.4)/√((0.4)(.6))/200

P[-0.08/0.0346410 < z < 0.08/0.0346410

P(−2.3094 < z < 2.3094)

P(z < -2.3094 ) - P(z < 2.3094)

0.98954 - 0.010461

= 0.97908

6 0

3 years ago